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oai:docta.ucm.es:20.500.14352/1045002025-03-18T15:38:45Zcom_20.500.14352_14col_20.500.14352_15

Solutions by Quadratures of Complex Bernoulli Differential Equations and Their Quantum Deformation Campoamor Stursberg, Otto-Rudwig Fernández Saiz, Eduardo Herranz, Francisco J. Nonautonomous differential equations Lie–Hamilton systems Book algebra Quantum groups Matemáticas (Matemáticas) 12 Matemáticas It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie–Hamilton system related to the book algebra b2 can always be solved by quadratures, providing an explicit solution of the equations. In addition, considering the quantum deformation of Bernoulli equations, their canonical form is obtained and an exact solution by quadratures is deduced as well. It is further shown that the approximations of k th-order in the deformation parameter from the quantum deformation are also integrable by quadratures, although an explicit solution cannot be obtained in general. Finally, the multidimensional quantum deformation of the book Lie–Hamilton systems is studied, showing that, in contrast to the multidimensional analogue of the undeformed system, the resulting system is coupled in a nontrivial form. Ministerio de Ciecia e Innovación Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub Descuento UCM 2024-05-28T13:42:07Z 2024-05-28T13:42:07Z 2023 journal article VoR https://hdl.handle.net/20.500.14352/104500 XXXX-XXXX 10.3390/axioms13010026 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-106802GB-I00/ES/GRUPO CUANTICOS, GRUPOS DE POISSON-LIE, ESPACIOS HOMOGENEOS Y APLICACIONES/ PRTR C17.I1 Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ open access application/pdf MDPI